Problem: On the first 6 tests of her geometry class, Tiffany got an average score of 82. What does she need on the next test to have an overall average of 84?
Let her score on the next test be $x$ The sum of all of her scores is then $6 \cdot 82 + x$ The same sum must also be equal to $7 \cdot 84$ Solve: $x = 7 \cdot 84 - 6 \cdot 82 = 96$.